It's a tradition amongst Vedic Astrologers to ask or call upon the blessings of the patron deity Ganesha. His power is to remove unseen obstacles and is called upon by many to bless any new beginning as well as to bring success in all endeavors. He was born a divine birth and is the son of Shiva and Parvati. Shiva is the male energy representing supreme consciousness and truth and Parvati is the female creative energy. Together these two energies gave birth to Ganesha, the remover of obstacles.
The myth of Ganesha's birth reveals the symbolism of his ability to remove ignorance or obstacles to learn truth, higher understanding, and wisdom. Hence he is associated with the planets that represent higher wisdom and spirituality Jupiter and Ketu. The myth goes like this: after attending a festival with her husband Shiva, Parvati was soiled from worldly activities and in need of a bath. Because Shiva was away and unable to stand guard outside her bath house, she created a son from the dirt off her body to protect the gate to her chamber. Meanwhile Shiva had returned to see his wife, but was stopped by an unknown boy guarding the entrance to Parvati's bathhouse. Not knowing Shiva was his father, Ganesha refused to let him pass. This infuriated Shiva and without a thought he severed the boy's head with his sword. Once Parvati realized what had happened, she demanded Shiva bring their son back to life. Shiva was instructed to find the head of the first animal he saw who was facing north and place it on the boy's head, thus Ganesha is known as the elephant headed God. The dirt on Parvati's body represents attachment to the world, Shiva's anger (mind) created ignorance and he was unable to see the truth. The act of removing Ganesha's head is a metaphor that truth cannot be known through the mind.
We can learn more about Ganesha's symbolism by looking at his picture. Each symbol represents an aspect of Ganesha's power, for example, the symbolism of him standing on a mouse reveals that Ganesha keeps desire and its by product greed, in check. He is the benevolent elephant that gently removes or places obstacles for our progress and protection.
To invoke Lord Ganesha, one can chant the short form of his mantra, "Om Gum Ganapataye Namaha" three times. His energies can also be invoked by chanting the seed sound for Ganesha, "GUM" 3, 9, 18, 27, 54 or 108 times. Thank him and ask him sincerely to remove both seen and unseen obstacles so you may succeed in your endeavors.
You do not need to be religious or a Hindu to chant mantras, it is not a religious act, rather it is an act of acknowledging a source energy and connecting to that energy in any form relevant to your belief system. The act of chanting a mantra is as simple as aligning oneself with a specific energy, and in this case, the energy is to remove the "unseen" obstacles as we make an effort to learn the science of Jyotish. Chanting is an act of humility, by chanting to Ganesha we acknowledge the power of the ego to hide the truth from ourselves and ask Ganesh to remove our ignorance.